Related papers: Fast Jacobian-Vector Product for Deep Networks
Deep Neural Networks (DNN) are crucial in approximating nonlinear functions across diverse applications, ranging from image classification to control. Verifying specific input-output properties can be a highly challenging task due to the…
Network Function Virtualization (NFV) is a promising virtualization technology that has the potential to significantly reduce the expenses and improve the service agility. NFV makes it possible for Internet Service Providers (ISPs) to…
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…
Deep learning involves a difficult non-convex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but…
Machine learning-based weather models have shown great promise in producing accurate forecasts but have struggled when applied to data assimilation tasks, unlike traditional numerical weather prediction (NWP) models. This study introduces…
To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that…
The Newton, Gauss--Newton and Levenberg--Marquardt methods all use the first derivative of a vector function (the Jacobian) to minimise its sum of squares. When the Jacobian matrix is ill-conditioned, the function varies much faster in some…
This study proposes a simple procedure to compute Efficient Pseudo Likelihood (EPL) estimator proposed by Dearing and Blevins (2024) for estimating dynamic discrete games, without computing Jacobians of equilibrium constraints. EPL…
Visual Autoregressive (VAR) modeling inefficiently applies a fixed computational depth to each position when generating high-resolution images. While existing methods accelerate inference by pruning tokens using frequency maps, their binary…
Speculative Jacobi Decoding (SJD) has emerged as a promising method for accelerating autoregressive image generation. Despite its potential, existing SJD approaches often suffer from the low acceptance rate issue of speculative tokens due…
A large item catalogue is a major challenge for deploying modern sequential recommender models, since it makes the memory footprint of the model large and increases inference latency. One promising approach to address this is RecJPQ, which…
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss--Markov prior and…
We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The…
The architectures of deep neural networks (DNN) rely heavily on the underlying grid structure of variables, for instance, the lattice of pixels in an image. For general high dimensional data with variables not associated with a grid, the…
Singular value decomposition (SVD) is widely used for dimensionality reduction and noise suppression, and it plays a pivotal role in numerous scientific and engineering applications. As the dimensions of the matrix grow rapidly, the…
We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under…
We propose a new way of constructing invertible neural networks by combining simple building blocks with a novel set of composition rules. This leads to a rich set of invertible architectures, including those similar to ResNets. Inversion…
Value Iteration Networks (VINs) have emerged as a popular method to incorporate planning algorithms within deep reinforcement learning, enabling performance improvements on tasks requiring long-range reasoning and understanding of…
Two harmonic extraction based Jacobi--Davidson (JD) type algorithms are proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair. They are called cross product-free (CPF) and inverse-free…
Image splicing is a very common image manipulation technique that is sometimes used for malicious purposes. A splicing detec- tion and localization algorithm usually takes an input image and produces a binary decision indicating whether the…